Alan

The correct equation is \(v = v_0 + at\)

Here \(v = 0m/s; a = -9.81m/s^2;t=4.5s \)

"A person moves 500 meters to the north, later changes direction and now moves 800 meters to the east. Determine the resultant displacement, as well as the angle and inclination of the resultant, with respect to the east."

Pythagoras gives:  d = sqrt(500^2 + 800^2) meters,    where d = displacement

Angle with respect to the east is given by tan^-1(500/800) radians

You can do the number crunching.

Pitágoras da: d = sqrt (500 ^ 2 + 800 ^ 2) metros, donde d = desplazamiento

El ángulo con respecto al este está dado por tan^-1 (500/800) radianes

Puedes hacer el cálculo de números.

H + 4 = J

J + 2 = 2(H + 2)  so J = 2H  + 2   Put this in the first equation:

H + 4 = 2H  + 2  so   H = 2,  Hence J = 6.

Not B.  There is no way you are going to get a negative term, when you multiply everything out, if both sets of parentheses contain only plus signs! 

Ok apart from the final step.  Should end up with r = 51/8

As follows:

I suspect this is meant to be as follows

This will be \(f(x) = (x-2-\sqrt2)(x-2+\sqrt2)(x-3-\sqrt6)(x-3+\sqrt6)\)

I'll leave you to multiply it out to confirm that it does indeed have rational coefficients.

Edit:  corrected signs.  Thanks to EP for making me aware of this.

v and u are at right angles, so v projected onto u is a zero length vector (i.e. the dot).

.w is in the opposite direction to u so the projection will be facing the opposite way from u (i.e. a)

x is a small amount in the same direction as u so its projection will be small and in the same direction as u (i.e. c)

I'll leave you to reason about te projection of y onto u.

I get the following: